Recent content by Pippi

Nice discussion. Who in geophysics and metereology are epitome of quality research and ethics?

What are the hottest topics in applied mathematics nowadays?

When I was studying electrical engineering in college, I stared at those CMOS equations and thought, "There is no rigor in physics."

Is it reasonable to guess that because nowadays, theories almost always precede the experiment and often cover contradictory outcomes, so we don't have such problems?

I am interested in a easy-to-read book on global geology and/or climate. The book will be ideal if it has discussions on how geology and climate changes, with detailed graphs (or data), due to seismic activities, external impacts like the solar wind from the Sun, and human-induced...

I am looking for an easy to read book on immunology that focuses on how diseases occur, progress, and cause changes at the cellular level in human body. The book will be ideal if it has a lot of pictures of affected human organs, graphs (or some representation of data in clinic), identification...

I am looking for a good textbook that can help developing intuition in algebra. I know a bit of number theory (Fermat's little theorem), algebra (up to fields), and topology. Are there good books that teach algebra with references to number theory and topology? I learned from Artin's...

Thanks but no thank you. You are not being helpful at all.

I don't know the right terminology. x_n represents a point in R^ω that has infinite number of coordinates. I want to use the sequence that if each of the coordinate converges as n grows large, x_n converges to a point. I want to show the difference between product topology and box topology...

Given the following sequence in the product space R^ω, such that the coordinates of x_n are 1/n, x1 = {1, 1, 1, ...} x2 = {1/2, 1/2, 1/2, ...} x3 = {1/3, 1/3, 1/3, ...} ... the basis in the box topology can be written as ∏(-1/n, 1/n). However, as n becomes infinitely large, the basis...

Ok, I see where my reasoning was wrong. The neighborhoods have to be open sets in this topology. If I pick two points, {0, 2}, in the open set (-inf, 1) U (1 inf), their neighborhoods can't be any open intervals and must be rays. Cheers!

I want to come up with examples that finite complement topology of the reals R is not Hausdorff, because by definition, for each pair x1, x2 in R, x1 and x2 have some disjoint neighborhoods. My thinking is as follows: finite complement topology of the reals R is a set that contains open sets...

Alright. Thank you for answering my question!

I am not asking what is more basic. For one, group theory does not explicitly say adding an infinite number of terms is NOT allowed. Just look at those textbook definitions. Second, if the definition does not explicitly say so, why can't I?

Rational numbers form a group under addition. However, a sequence of rational numbers converges to irrational number. Presumably, group theory does not allow adding an infinite number of rational numbers. This is not indicated in the textbook definition of a group. I might be looking in vain...